This paper addresses the concept of partial stabilization for driftless control systems called ”nonholonomic systems”. We introduce a class of feedback transformations that transforms our system in to a multi-chained triangular form. We show that we can bounded the first component; this can be done by using a smooth feedback control depending on the state. In addition the (n − 1) other componen...

This paper presents a geometric description on Lie algebroids of Lagrangian systems subject to nonholonomic constraints. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable...

This paper investigates the problem of finite-time state feedback stabilization for nonholonomic mobile robot with stochastic disturbance in the forward velocity. First of all, an appropriate state/input transformation is introduced to convert the mentioned control model into stochastic nonholonomic system in chain form. Then, by using stochastic finite-time stability theorem and the method of ...

This paper develops a constructive method for nding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior di erential systems. The results are applied to the problem of nding a set of nilpotent input vector elds for a nonholonomic control system, which can then used to constru...

In this paper we derive variational integrators for optimal control problems of nonholonomic mechanical systems. We rewrite the system as a constrained second-order variational problem, that is, as a problem where the Lagrangian and constraints are defined in terms of the position, velocity and the acceleration of the system. Instead of discretizing directly the equations of motion, we discreti...

This paper is concerned with iterative learning control of Hamiltonian systems with nonholonomic constraints. The author has proposed a novel iterative learning control method based on the symmetric property of Hamiltonian control systems. Unfortunately, however, it is not applicable to nonholonomic systems. The present paper proposes a set of feedback and coordinate transformations converting ...

This paper considers the position control problem of nonholonomic mobile robots with plant uncertainties and external disturbances. A robust passivity-based controller using fuzzy logic is proposed based on the reduced-form dynamic model of nonholonomic systems. The fuzzy logic system, whose parameters are tuned on-line, is introduced to learn the unknown (uncertain) plant dynamics due to the u...

The stabilization to a desired pose of a nonholonomic mobile robot, based on visual data from a hand-eye system mounted on it, is considered. Instances of this problem occur in practice during docking or parallel parking maneuvers of such vehicles. In this paper, we investigate the use of visual servoing techniques for their control. After brie y presenting the relevant visual servoing framewor...

In this paper, nonholonomic gerbes will be naturally derived for manifolds and vector bundle spaces provided with nonintegrable distributions (in brief, nonholonomic spaces). An important example of such gerbes is related to distributions defining nonlinear connection (N–connection) structures. They geometrically unify and develop the concepts of Riemann–Cartan manifolds and Lagrange–Finsler sp...

Virtual master-slave concept is proposed to realize a human-machine interface for nonholonomic systems. In this concept, the virtual master system acts as an interface to control the slave system. The control architecture using this concept is based on a two degrees-of-freedom (DOF) design, where the neural network (NN) constructs a feedforward controller, whereas a compensator acts as a feedba...